1. Field of the Invention
The present invention relates to tiles for covering a plane surface, and more particularly, to the field of geometry known as tessellation, which has been defined as the covering of prescribed areas with tiles of prescribed shapes. Practical applications of this field include the design of paving and of wall-coverings, educational toys and games, and artistic creations which have esthetic appeal to the beholder
2. Discussion of the Relevant Art
In the general field of tessellation, symmetry obviously plays an important part. The simplest and best-known form of tessellation is the jig-saw puzzle, in which a very simple shape, such as a rectangle or a circle, is covered with a multitude of pieces of irregular shapes and may have indicia thereon in the form of a design or picture. The characteristic of a jig-saw puzzle is the fact that it is designed to be assembled in a particular manner in order to be able to recover a complete picture from the various portions that have been placed on each of the individual pieces. A recent form of tessellation is disclosed in U.S. Pat. No. 4,133,152 to Penrose. The tiles of Penrose are generally composed of two types. Each type is basically quadrilateral in shape and the respective shapes are such that if a multiplicity of tiles are juxtaposed in a matching configuration, which may be prescribed by matching markings or shapings, the pattern which they form is necessarily non-repetitive (non-periodic), giving a considerable esthetic appeal in the eye of the beholder.
More sophisticated forms of tessellation have utilized identical pieces which may be arranged to form a variety of shapes, such as so-called polyominoes. One of these tessellation arrangements is disclosed in U.S. Pat. No. 4,223,890 to Schoen which issued on Sept. 23, 1980, which discloses the use of a set of tiles composed of distinct pieces which can be arranged in a variety of ways to form the identical regular polygon having an even number of sides. While the set may be constructed relatively easily, the number of ways in which the regular polygon may be formed therefrom increases rapidly for increasing numbers of sides of the polygon. Sets of tiles according to the invention may be used to constrct different puzzles; each having widely differing complexity. The tiles may also be adapted to be used as a game, for educational purposes, and in the arrangement of esthetic designs.
The present invention differs from all tessellation schemes known in the prior art, in that the tiles are preferably identical in shape and may be juxtaposed to cover a plane surface while creating a periodic or non-periodic design. Utilizing different types of indicia on the tiles permits numerous varying effects to be accomplished which are appealing to the beholder. With modification of the conventional straight line side the tiles may be made to form fish or fowl and combined in any determined proportion to create a further striking affect. The number of sides utilized in the construction of a tile is always an odd integer and may be any number greater than 5.